Yuri Nikolayevsky




La Trobe Mathematics and Statistics Official Home Page



Office:         Room 217, Physical Sciences 2
Address:    Department of Mathematics and Physics, La Trobe University, Melbourne, Victoria 3086, Australia
Phone:        +61 (03) 9479 1644
Email:         

 

Research interests
  • Lie groups and Lie algebras, homogeneous spaces and symmetric spaces.
  • Riemannian geometry, geometry of submanifolds, integral and conformal geometry. 
  • Topological graph theory.
Looking for a PhD supervisor?

Contact me. General information: Postgraduate studies at La Trobe University.

Publications and preprints

  1. with J.A.Wolf, The Structure of Geodesic Orbit Lorentz Nilmanifolds. (preprint)
  2. with G.Cairns, Respectful decompositions of Lie algebras. (preprint)
  3. with An Ky Nguyen, Stability of geodesic vectors in low-dimensional Lie algebras. (preprint)
  4. with J.H.Park, Einstein hypersurfaces in irreducible symmetric spaces. (preprint)
  5. with Y.Euh, J.Kim, J.H.Park, On 2-stein submanifolds in space forms. Results Math. 77 (2022), 84, doi: 10.1007/s00025-022-01620-9 (preprint)
  6. with S.Kim, J.H.Park, Einstein hypersurfaces of Damek-Ricci spaces.  J. Geom. Phys. 167 (2021), 104278,  doi: 10.1016/j.geomphys.2021.104278. (preprint)
  7. with Z. Chen, Yu. Nikonorov, Compact geodesic orbit spaces with a simple isotropy group. (preprint)
  8. O.Dearricott, W.Tuschmann, Y.Nikolayevsky, T.Leistner, D.Crowley (Eds.) Differential Geometry in the Large (London Mathematical Society Lecture Note Series). Cambridge: Cambridge University Press, 463 (2020).
  9. with G.Cairns, B.Jessup, A class of nilpotent Lie algebras whose center acts nontrivially in cohomology. Proc. Amer. Math. Soc. 148 (2020), 1945-1952. (preprint)
  10. with G.Cairns, E.Groves, Bad drawings of small complete graphs. Australas. J. Comb. 75(3) (2019), 322-342. (preprint)
  11. with S.Kim, J.H.Park, Einstein hypersurfaces of the Cayley projective plane. Diff. Geom. Appl. 69 (2020), doi: 10.1016/j.difgeo.2020.101594. (preprint)
  12. with S.Kim, J.H.Park, Totally geodesic submanifolds of Damek-Ricci spaces. Rev. Mat. Iberoam. 37 (2021), 1321-1332, doi: 10.4171/rmi/1228. (preprint)
  13. with D.Alekseevsky, Einstein extensions of Riemannian manifolds. Trans. Amer. Math. Soc. 374 (2021), 6059-6083. (preprint)
  14. Geodesic orbit and naturally reductive nilmanifolds associated with graphs. Math. Nachr. 293 (2020), 754-760. (preprint)
  15. with A.Borisenko, On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space. J. Geom. Phys. 155 (2020), doi: 10.1016/j.geomphys.2020.103776. (preprint)
  16. with P.Adams, Planar bipartite biregular degree sequences. Discrete Math. 342 (2019), 433-440. (preprint)
  17. with G.Misereh, Annular and pants thrackles. Discrete Math. Theor. Comput. Sci. 20:1 (2018), #16, 17 pp.
  18. with Yu.Nikonorov, On invariant Riemannian metrics on Ledger-Obata spaces. manuscripta math. 158 (2019), 353-370. (preprint)
  19. with W.Globke, Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension. Diff. Geom. Appl. 54B (2017), 475-489. (preprint)
  20. with G.Misereh, Thrackles containing a standard musquash. Australas. J. Comb. 70 (2018), 168–184. (preprint)
  21. with V.Matveev, Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties. Ann. Inst. Fourier, 67 (2017), 843-862. (preprint)
  22. with G.Cairns, A.Hinić Galić, Curvature properties of metric nilpotent Lie algebras which are independent of metric. Ann. Global Anal. Geom. 51 (2017), 305-325. (preprint)
  23. with I.Tsartsaflis, Cohomology of ℕ-graded Lie algebras of maximal class over ℤ2. J. Lie Theory, 27 (2017), 529-544. (preprint)
  24. with J.H.Park, H-contact unit tangent sphere bundles of Riemannian manifolds. Diff. Geom. Appl. 49 (2016), 301–311. (preprint)
  25. with Z.Rakić, The Duality principle for Osserman algebraic curvature tensors. Linear Algebra Appl. 504 (2016), 574-580. (preprint)
  26. with G.Cairns, S.Mendan, A sufficient condition for a pair of sequences to be bipartite graphic. Bull. Austral. Math. Soc. 94 (2016), 195-200. (preprint)
  27. with G.Cairns, G.Rossiter, Conewise linear periodic maps of the plane with integer coefficients. Amer. Math. Monthly, 123 (2016), 363-375. (preprint)
  28. Solvable extensions of negative Ricci curvature of filiform Lie groups. Math. Nachr. 289 (2016), 321-331. (preprint)
  29. with G.Cairns, T.Koussas, Great-circle spherical Thrackles. Discrete Math. 338 (2015), 2507-2513. (preprint)
  30. with V.Matveev, A counterexample to Belgun-Moroianu conjecture. C.R. Acad. Sci. Paris Sér. I Math. 353 (2015), 455–457. (preprint)
  31. Totally geodesic hypersurfaces of homogeneous spaces. Israel J. Math. 207 (2015), 361-375. (preprint)
  32. with Yu.Nikonorov, Solvable Lie groups of negative Ricci curvature. Math. Z. 280 (2015), 1-16. (preprint)
  33. with G.Cairns, A.Hinić Galić, I.Tsartsaflis, Geodesic bases for Lie algebras. Linear Multilinear Algebra, 63 (2015), 1176-1194. (preprint)
  34. with G.Cairns, S.Mendan, A sharp refinement of a result of Zverovich - Zverovich. Discrete Math. 338 (2015), 1085-1089. (preprint)
  35. with G.Cairns, S.Mendan, A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences. Australas. J. Combin. 60 (2014), 217-226. (preprint)
  36. with G.Cairns, N.T.Tung Le, A.Nielsen, On the existence of orthonormal geodesic bases for Lie algebras. Note Mat. 33 (2013), 11-18. (preprint)
  37. with Z.Rakić, A note on Rakić duality principle for Osserman manifolds. Proc. 17 Geom. Seminar Zlatibor, 2012. Publ. Inst. Math., Nouv. Ser. 94 (108) (2013), 43-45. (preprint)
  38. Weyl-Schouten Theorem for symmetric spaces. Proc. London Math. Soc. 107 (2013), 151-176. (preprint)
  39. with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of filiform nilpotent Lie algebras.  J. Lie Theory, 23 (2013), 1051-1074. (preprint)
  40. with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of nilpotent Lie algebras. J. Lie Theory, 23 (2013), 1023-1049. (preprint)
  41. Einstein solvmanifolds attached to two-step nilradicals. Math. Z. 272 (2012), 675-695. (preprint) 
  42. Conformally Osserman manifolds of dimension 16 and Weyl-Schouten Theorem for rank-one symmetric spaces. Ann. Mat. Pura Appl. 191 (2012), 677-709. (preprint)
  43. with G.Cairns, Outerplanar Thrackles. Graphs Combin. 28 (2012), 85-96.
  44. Einstein solvmanifolds and the pre-Einstein derivation. Trans. Amer. Math. Soc. 363 (2011), 3935-3958. (preprint)
  46. Conformally Osserman manifolds. Pacific J. Math. 245 (2010), 315-358. (preprint) 
  47. with G.Cairns, Generalized Thrackle Drawings of Non-Bipartite Graphs. Discrete Comput. Geom. 41 (2009), 119-134.
  49. Einstein solvmanifolds with free nilradical  Ann. Global Anal. Geom. 33 (2008), 71-87. (preprint)
  50. with J. Banks, G. Cairns, M. Jackson, M. Jerie, T. Poole, On the definition of topology – a cautionary tale. Austral. Math. Soc. Gaz. 35 (2008), 195-202.
  51. On Osserman manifolds of dimension 16. Contemporary Geometry and Related Topics, Proc. Conf. Belgrade, 2005 (2006), 379-398.
  52. Two theorems on harmonic manifolds. Comm. Math. Helv. 80 (2005), 29-50. (preprint) 
  53. Osserman Conjecture in dimension n ≠ 8, 16. Math. Ann. 331 (2005), 505-522. (preprint)
  55. Osserman manifolds of dimension 8. Manuscripta Math. 115 (2004), 31-53. (preprint)
  56. with G.Cairns, M.McIntyre, The Thrackle conjecture for K5 and K3,3. Towards a theory of geometric graphs, 35-54, Contemp. Math., 342, Amer. Math. Soc., 2004.
  57. Two theorems on Osserman manifolds. Differential Geom. Appl. 18 (2003), 239-253.
  58. Osserman manifolds and Clifford structures. Houston J. Math. 29 (2003), 59-75.
  59. with P.J.Forrester, D.S.McAnally, On the evaluation formula for Jack polynomials with prescribed symmetry. J. Phys. A. 34 (2001), 8407-8424.
  60. Surfaces with simple geodesics. Tsukuba J. Math. 24 (2000), 233-247. (preprint)
  61. with G.Cairns, Bounds for generalized thrackles. Discrete Comput. Geom. 23 (2000), 191-206.
  63. with R.Langevin, Three viewpoints on the integral geometry of foliations. Illinois J. Math. 43 (1999), 233-255.
  64. Non-immersion theorem for a class of hyperbolic manifolds. Diff. Geom. Appl. 9 (1998), 239-242.
  65. Totally umbilical submanifolds in G(2,n). IV. Math. Fiz. Anal. Geom. 5 (1998), 95-113. (читать по-русски)
  67. Totally umbilical submanifolds in G(2,n). III. Math. Fiz. Anal. Geom. 3 (1996), 339-355. (читать по-русски)
  68. On Fenchel's problem. Mat. Zametki 56 (1994), 87 – 97; translation in Math. Notes 56 (1994), 1158-1164.
  69. Totally umbilical submanifolds of symmetric spaces. Math. Fiz. Anal. Geom. 1 (1994), 314-357.
  70. Extrinsic spheres in a symmetric space. Mat. Zametki 51 (1992), 72-76; translation in Math. Notes 51 (1992), 155-158. (читать по-русски)
  71. Classification of multidimensional submanifolds in a Euclidean space with a totally geodesic Grassmann image. Math. USSR Sb. 183 (1992), 127-154; translation in Russian Acad. Sci. Sb. Math. 76 (1993), 225-246. (читать по-русски)
  72. with A.Borisenko, Grassmann manifolds and Gauss image of submanifolds. Uspekhi Mat. Nauk 46 (1991), 41-83; translation in Russian Math. Surveys 46 (1991), 45-94. (читать по-русски)
  73. Totally umbilical submanifolds in G(2,n). II. Ukrain. Geom. Sb. 35 (1992), 83-99; translation in J. Math. Sci. 72 (1994), 3212-3222.
  74. Totally umbilical submanifolds in G(2,n). I. Ukrain. Geom. Sb. 34 (1991), 83-98 ; translation in J. Math. Sci. 69 (1994), 888-899.
  75. Submanifolds of Euclidean space with a totally geodesic Gauss image. Dokl. Akad. Nauk SSSR 314 (1990), 297-300; translation in Soviet Math. Dokl. 42 (1991), 456-459.
  76. Surfaces for which the curvature of the Grassmannian image is at least 1. Ukrain. Geom. Sb. 33 (1990), 77-91; translation in J. Soviet Math. 53 (1991), 516-526.
  77. with A.Borisenko, Surfaces with maximal curvature of the Grassmann image. Mat. Zametki 48 (1990), 12-19; translation in Math. Notes 48 (1990), 880-885. (читать по-русски)
  78. with A.Borisenko, Classification of the points of three-dimensional surfaces according to the Grassmann image. Ukrain. Geom. Sb. 32 (1989), 11-27; translation in J. Soviet Math. 59 (1992), 697-709.
  79. with A.Borisenko, Algebraic surfaces defined by a homogeneous polynomial. Ukrain. Geom. Sb. 30 (1987), 3-10; translation in J. Sov. Math. 51 (1990), 2497-2502.  
To the official home page of the Department of Mathematics and Statistics.